Finite Group Databasebeta

← #6640591

Subgroups — #6640591

Order 512.

1591 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37271C211yesmaximal, characteristic
2#35263C211yesmaximal, characteristic, complemented
3#32985C211yesmaximal, characteristic, complemented
4#32981C211yesmaximal, characteristic, complemented
5#32277C211yesmaximal, characteristic, complemented
6#32271C211yesmaximal, characteristic, complemented
7#32266C211yesmaximal, characteristic, complemented
8#32260C211yesmaximal, characteristic, complemented
9#32042C211yesmaximal, characteristic, complemented
10#32041C211yesmaximal, characteristic, complemented
11#32032C211yesmaximal, characteristic, complemented
12#32031C211yesmaximal, characteristic, complemented
13#32023C211yesmaximal, characteristic, complemented
14#32022C211yesmaximal, characteristic, complemented
15#32012C211yesmaximal, characteristic, complemented
16#32011C211yesmaximal, characteristic, complemented
17#32007C211yesmaximal, characteristic, complemented
18#32006C211yesmaximal, characteristic, complemented
19#31996C211yesmaximal, characteristic, complemented
20#31995C211yesmaximal, characteristic, complemented
21#29894C211yesmaximal, characteristic, complemented
22#29892C211yesmaximal, characteristic, complemented
23#27623C211yesmaximal, characteristic, complemented
24#27621C211yesmaximal, characteristic, complemented
25#24569C211yesmaximal, characteristic, complemented
26#24569C211yesmaximal, characteristic, complemented
27#24567C211yesmaximal, characteristic, complemented
28#24565C211yesmaximal, characteristic, complemented
29#24075C211yesmaximal, characteristic, complemented
30#24075C211yesmaximal, characteristic, complemented
31#21744C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#408C2211yescharacteristic
40C2×#408C2211yescharacteristic
41#2855—21no—
42#2854—21no—
43#2848C2211yescharacteristic
44#2847C2211yescharacteristic
45#2723—21no—
46#2714—21no—
47#2710—21no—
48#2706—21no—
49#2692—21no—
50#2678—21no—
51#2676—21no—
52#2670—21no—
53#2625—21no—
54#2624—21no—
55#2616C2211yescharacteristic
56#2615C2211yescharacteristic
57#2563C2211yescharacteristic
58#2547C2211yescharacteristic
59#2540C2211yescharacteristic
60#2540C2211yescharacteristic
61#2538C2211yescharacteristic
62#2537C2211yescharacteristic
63#2536C2211yescharacteristic
64#2535C2211yescharacteristic
65#2498—21no—
66#2498—21no—
67#2487C2211yescharacteristic
68#2487C2211yescharacteristic
69#2486C2211yescharacteristic
70#2486C2211yescharacteristic
71#2485C2211yescharacteristic
72#2485C2211yescharacteristic
73#2485C2211yescharacteristic
74#2485C2211yescharacteristic
75#2412—21no—
76#2412—21no—
77#2316C2211yescharacteristic
78#2316C2211yescharacteristic
79#2314C2211yescharacteristic
80#2311C2211yescharacteristic
81#2311C2211yescharacteristic
82C2×#380C2211yescharacteristic
83#2101C2211yescharacteristic, complemented
84#2101C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2085C2211yescharacteristic, complemented
88#2085C2211yescharacteristic, complemented
89#2084C2211yescharacteristic, complemented
90#2084C2211yescharacteristic, complemented
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2076C2211yescharacteristic, complemented
102#2076C2211yescharacteristic, complemented
103#2076C2211yescharacteristic, complemented
104#2075C2211yescharacteristic
105#2075C2211yescharacteristic
106#2075C2211yescharacteristic, complemented
107#2058C2211yescharacteristic, complemented
108#2058C2211yescharacteristic, complemented
109#2057C2211yescharacteristic, complemented
110#2057C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2042C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2042C2211yescharacteristic, complemented
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2035C2211yescharacteristic, complemented
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic, complemented
128#2034C2211yescharacteristic, complemented
129#2033C2211yescharacteristic, complemented
130#2033C2211yescharacteristic, complemented
131#1921C2211yescharacteristic, complemented
132#1920C2211yescharacteristic, complemented
133#1920C2211yescharacteristic, complemented
134#1920C2211yescharacteristic, complemented
135#1919C2211yescharacteristic, complemented
136#1919C2211yescharacteristic, complemented
137#1919C2211yescharacteristic, complemented
138#1918C2211yescharacteristic, complemented
139#1895C2211yescharacteristic, complemented
140#1895C2211yescharacteristic, complemented
141#1894C2211yescharacteristic, complemented
142#1894C2211yescharacteristic, complemented
143#1893C2211yescharacteristic, complemented
144#1893C2211yescharacteristic, complemented
145#1892C2211yescharacteristic, complemented
146#1892C2211yescharacteristic, complemented
147#1875C2211yescharacteristic
148#1875C2211yescharacteristic
149#1874C2211yescharacteristic
150#1874C2211yescharacteristic
151#1874C2211yescharacteristic
152#1874C2211yescharacteristic
153#1873C2211yescharacteristic
154#1873C2211yescharacteristic
155#1872C2211yescharacteristic
156#1872C2211yescharacteristic
157#1872C2211yescharacteristic
158#1872C2211yescharacteristic
159#1870C2211yescharacteristic
160#1870C2211yescharacteristic
161#1870C2211yescharacteristic
162#1870C2211yescharacteristic
163#1869C2211yescharacteristic
164#1869C2211yescharacteristic
165#1869C2211yescharacteristic
166#1869C2211yescharacteristic
167#1865C2211yescharacteristic, complemented
168#1865C2211yescharacteristic, complemented
169#1864C2211yescharacteristic, complemented
170#1864C2211yescharacteristic, complemented
171#1863C2211yescharacteristic, complemented
172#1863C2211yescharacteristic, complemented
173#1862C2211yescharacteristic, complemented
174#1862C2211yescharacteristic, complemented
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic
190#1825C2211yescharacteristic
191#1818C2211yescharacteristic
192#1818C2211yescharacteristic
193#1809C2211yescharacteristic, complemented
194#1809C2211yescharacteristic, complemented
195#1809C2211yescharacteristic, complemented
196#1809C2211yescharacteristic, complemented
197#1808C2211yescharacteristic, complemented
198#1807C2211yescharacteristic, complemented
199#1807C2211yescharacteristic, complemented
200#1807C2211yescharacteristic, complemented
201#1779C2211yescharacteristic
202#1779C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#542—42no—
210#542—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#124—21no—
214C2×#124—21no—
215C2×#124C2311yescharacteristic
216#525—42no—
217#525—42no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123D411yescharacteristic
222C2×#123D411yescharacteristic
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8D411yescharacteristic
225C2×C22⋊Q8D411yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121D411yescharacteristic
233C2×#121D411yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120D411yescharacteristic
241C2×#120D411yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C2×#117—21no—
250C2×#117—42no—
251C2×#117—42no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C42—21no—
264#485—42no—
265#485—42no—
266#482—42no—
267#482—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300#408—42no—
301#408—42no—
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318#400—21no—
319#400—21no—
320#399—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#392—21no—
353#392—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#392—21no—
358#391—21no—
359#391—21no—
360#391—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384C2311yescharacteristic
413#382—21no—
414#382C2311yescharacteristic
415#381—21no—
416#381—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C2×#95—21no—
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25C2×D411yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8C2×D411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4C2×D411yescharacteristic
506C22×D4C2×D411yescharacteristic
507C22×D4C2×D411yescharacteristic
508C22×D4C2×D411yescharacteristic
509C22×D4C2×D411yescharacteristic
510C22×D4C2×D411yescharacteristic
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4—41no—
523C23×C4—41no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C22×C8—41no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554#126—44no—
555#124—41no—
556#124—41no—
557#124—44no—
558#124—82no—
559#123—42no—
560#123—42no—
561#123—44no—
562#123—82no—
563#123—82no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—42no—
567C22⋊Q8—42no—
568C22⋊Q8—44no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577#121—22no—
578#121—22no—
579#121—42no—
580#121—42no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—82no—
590#120—42no—
591#120—42no—
592#120—82no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—41no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—44no—
616#117—44no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—44no—
706C2×C22⋊C4—82no—
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—44no—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#107—41no—
732#107—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736#106—41no—
737#106—41no—
738#106—41no—
739#106—41no—
740#106—41no—
741#106—41no—
742#106—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809C24—22no—
810C24—22no—
811C24—21no—
812C24—41no—
813C24—41no—
814C24—41no—
815C24—41no—
816C24—41no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C24C22×D411yescharacteristic
821C24C22×D411yescharacteristic
822#41—82no—
823#41—82no—
824#41—82no—
825#41—82no—
826C2×Q8—22no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—41no—
834C2×Q8—41no—
835C2×Q8—42no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4H(5,𝔽2)12yes—
961C22×C4H(5,𝔽2)12yes—
962C22×C4C2511yescharacteristic
963M16—82no—
964M16—82no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—82no—
990C2×C8—82no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—81no—
1105C42—81no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—44no—
1140C23—44no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—82no—
1149C23—82no—
1150C23—82no—
1151C23—82no—
1152C23—82no—
1153C23#53412yes—
1154C23#57712yes—
1155C23C23×D411yescharacteristic
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—82no—
1161Q8—162no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—82no—
1167D4—82no—
1168D4—82no—
1169D4—82no—
1170D4—82no—
1171D4—82no—
1172D4—82no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—44no—
1209C2×C4—44no—
1210C2×C4—44no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4#53412yes—
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C2×C4#58511yescharacteristic
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—88no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22C2×#53411yescharacteristic
1336C22#348511yescharacteristic
1337C22#348511yescharacteristic
1338C22C2×#57711yescharacteristic
1339C22#358411yescharacteristic
1340C22#358511yescharacteristic
1341C22#358611yescharacteristic
1342C4—22no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4#353311yescharacteristic
1367C4#353311yescharacteristic
1368C4#353311yescharacteristic
1369C4#353311yescharacteristic
1370C2—42no—
1371C2—42no—
1372C2—81no—
1373C2—81no—
1374C2—81no—
1375C2—161no—
1376C2#3695511yescharacteristic
1377C2#6076511yescharacteristic
1378C2#6076611yescharacteristic
1379C2#6175511yescharacteristic
1380C2#6176211yescharacteristic
1381C2#6177011yescharacteristic
1382C2#6178211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37271C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#525 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #35263C2semidirect
3. #32985C2semidirect
4. #32981C2semidirect
5. #32277C2semidirect
6. #32271C2semidirect
7. #32266C2semidirect
8. #32260C2semidirect
9. #32042C2semidirect
10. #32041C2semidirect
11. #32032C2semidirect
12. #32031C2semidirect
13. #32023C2semidirect
14. #32022C2semidirect
15. #32012C2semidirect
16. #32011C2semidirect
17. #32007C2semidirect
18. #32006C2semidirect
19. #31996C2semidirect
20. #31995C2semidirect
21. #29894C2semidirect
22. #29892C2semidirect
23. #27623C2semidirect
24. #27621C2semidirect
25. #24569C2semidirect
26. #24569C2semidirect
27. #24567C2semidirect
28. #24565C2semidirect
29. #24075C2semidirect
30. #24075C2semidirect
31. #21744C2semidirect
83. #2101C22semidirect
84. #2101C22semidirect
85. #2100C22semidirect
86. #2099C22semidirect
87. #2085C22semidirect
88. #2085C22semidirect
89. #2084C22semidirect
90. #2084C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
101. #2076C22semidirect
102. #2076C22semidirect
103. #2076C22semidirect
106. #2075C22semidirect
107. #2058C22semidirect
108. #2058C22semidirect
109. #2057C22semidirect
110. #2057C22semidirect
111. #2042C22semidirect
112. #2042C22semidirect
113. #2042C22semidirect
114. #2042C22semidirect
119. #2035C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
122. #2035C22semidirect
127. #2034C22semidirect
128. #2034C22semidirect
129. #2033C22semidirect
130. #2033C22semidirect
131. #1921C22semidirect
132. #1920C22semidirect
133. #1920C22semidirect
134. #1920C22semidirect
135. #1919C22semidirect
136. #1919C22semidirect
137. #1919C22semidirect
138. #1918C22semidirect
139. #1895C22semidirect
140. #1895C22semidirect
141. #1894C22semidirect
142. #1894C22semidirect
143. #1893C22semidirect
144. #1893C22semidirect
145. #1892C22semidirect
146. #1892C22semidirect
167. #1865C22semidirect
168. #1865C22semidirect
169. #1864C22semidirect
170. #1864C22semidirect
171. #1863C22semidirect
172. #1863C22semidirect
173. #1862C22semidirect
174. #1862C22semidirect
193. #1809C22semidirect
194. #1809C22semidirect
195. #1809C22semidirect
196. #1809C22semidirect
197. #1808C22semidirect
198. #1807C22semidirect
199. #1807C22semidirect
200. #1807C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#372712
#352632
#329852
#329812
#322772
#322712
#322662
#322602
#320422
#320412
#320322
#320312
#320232
#320222
#320122
#320112
#320072
#320062
#319962
#319952
#298942
#298922
#276232
#276212
#245692
#245672
#245652
#240752
#217442